The atomic force microscope (AFM) is increasingly becoming a first line tool for measuring material properties at microscopic scales. When it comes to soft biological materials such as cells, however, serious problems have been identified with both the widely used measuring approach and with the data analysis methods. Here we develop an improved experimental approach and develop the theoretical framework for the analysis of collected AFM force-displacement data. We also establish the applicability domain for both the experimental and theoretical frameworks. The results of the project are being verified by extracting elastic moduli for soft gels using the AFM and then comparing those results with those obtained from macroscopic measurements.